President Trump’s deliberations over a Supreme Court nominee now center on three candidates culled from his shortlist: federal judges Brett M. Kavanaugh, Raymond Kethledge and Amy Coney Barrett, according to White House officials and Trump advisers involved in the discussions.

But Trump’s final decision on a replacement for Justice Anthony M. Kennedy remained fluid as he traveled Thursday to a political rally in Montana before heading to his golf course in New Jersey for the weekend, with the president pinballing between associates as he sought feedback and suggestions.

While Trump has placed Kavanaugh, a polished former Kennedy clerk and Yale Law School graduate, near the top of his list, he has also been asking several friends and aides about whether Kavanaugh’s past work in President George W. Bush’s White House would be an issue for his core supporters, thousands of whom filled the Four Seasons Arena in Great Falls, Mont., on Thursday evening.

And Trump is hearing out arguments for Kethledge, another former Kennedy clerk, and for Coney Barrett, a University of Notre Dame Law School professor who is being championed by some social conservatives, according to the advisers, who requested anonymity because they were not authorized to speak publicly.

Kavanaugh and Kethledge have the “inside track,” according to a person close to the president, because some White House officials believe Coney Barrett, 46, could instead be a pick for the high court in the coming years, after she gains more experience on the federal bench.

A second person close to the president said Thursday that Kavanaugh and Kethledge are the shortlist.

Vice President Pence met privately with Kavanaugh on Wednesday at the vice president’s residence and that session went well, underscoring the judge’s strong prospects, according to two Republicans briefed on the meeting.

“I think I have it down to four people, and I think of the four people, I have it down to three or two. I think they’re all outstanding,” Trump told reporters Thursday en route to Montana, declining to name the finalists. “I don’t want to say the four. But I have it down to four. I’ll have a decision made in my mind by Sunday. We’ll announce it on Monday.”

Others who emerged on Trump’s shortlist just days ago — federal judges Thomas M. Hardiman, Amul R. Thapar and Joan L. Larsen, as well as Sen. Mike Lee (R-Utah) — remain in contention, but the president’s queries have mostly been about the leading contenders, whether it’s been during phone calls, in Oval Office meetings or on Air Force One.

One Trump adviser said the president is unlikely to expand his list in the coming days but could follow up by phone with some of the candidates, all of whom have been asked to fill out disclosure forms dealing with their finances and conduct.

Trump told reporters he did not expect to bring candidates in for interviews again when he headed to his New Jersey golf club this weekend. “I doubt it,” he said.

Trump’s process has echoes of his search for a Supreme Court justice last year — he eventually nominated Neil M. Gorsuch — and his consideration of a running mate during the 2016 presidential campaign. Even as White House counsel Donald McGahn fiercely guarded information about the candidate interviews and Trump’s leanings, the president was engaging with the freewheeling loop of boosters, lawmakers and confidants that he has long counted on for political gut checks.

“Do you know him?” Trump has asked about Kethledge, advisers said. Or, on Kavanaugh’s link to the Bush network, with which Trump has clashed for years, the president has flatly asked, “What do you think?”

Others close to Trump said a variety of factors was on the president’s radar beyond the candidates’ interpretation of the law, such as their educational profiles, personal backgrounds and rapport with him in interviews — leaving most Trump allies wary of making predictions.

“He listens to everybody, big or small, influential or not, and absorbs it all,” said Trump friend and Newsmax chief executive Christopher Ruddy. “He then adds that to how he feels and comes to a conclusion.”

The resignation Thursday of Scott Pruitt, the administrator of the Environmental Protection Agency, after months of scrutiny over ethics issues added some uncertainty to Trump’s timeline for a Supreme Court decision. As White House officials handled Pruitt’s exit, some Trump allies wondered whether the president might announce his choice before Monday to bump Pruitt from the headlines.

Trump, however, maintained Thursday that Monday remains his chosen date for an announcement. “We’re going to do it at 9 p.m. in the White House,” he told reporters.

Debates over Kavanaugh’s work with Bush and rulings he has made on health care and abortion continued to churn Thursday as critics urged the president to shy away from a judge with an establishment Republican pedigree.

Kavanaugh, 53, helped investigate President Bill Clinton as part of independent counsel Kenneth W. Starr’s team and then served as an aide to Bush before joining the U.S. Court of Appeals for the D.C. Circuit in 2006.

“He looks, walks and quacks like John G. Roberts Jr.,” said former Virginia attorney general Ken Cuccinelli II, referencing the chief justice of the United States, who angered conservatives with his rulings on President Barack Obama’s signature health-care law. “The Bush lives loudly in Kavanaugh.”

Cuccinelli’s remark was a wry reference to another contender, Coney Barrett, whom social conservatives unsure about Kavanaugh have rallied behind this week.

“The dogma lives loudly within you,” Sen. Dianne Feinstein (D-Calif.) told Coney Barrett last year during her confirmation hearing in an exchange about the judge’s Catholic faith — a comment that was roundly criticized by religious leaders.

“If Democrats tried to go anti-Catholic with her, that’d backfire and we know it,” said Rep. Peter T. King (R-N.Y.).

But Trump is not rushing toward Coney Barrett with the same fervor, according to two people close to the president. They described his view of her as “positive,” since he appointed her, but noted that he sees Kavanaugh and Kethledge as similar to Gorsuch, another former Kennedy clerk, whose tenure has been celebrated by his supporters and whose judicial records are largely acceptable to most wings of the Republican Party.

Sen. Rand Paul (R-Ky.), a Trump ally, signed a statement Thursday with other conservative leaders pushing for Lee, after days of phone calls with Trump and others over his concerns about Kavanaugh. The move complicated the outlook in the Senate, where Republicans have a narrow, 51-seat majority.

Kethledge’s sudden ascent in the process is widely seen in the West Wing as a consequence of what conservative talk-radio host Rush Limbaugh has called the “whisper campaign” against Kavanaugh, with the president newly intrigued by the University of Michigan Law School graduate.

Democrats, meanwhile, prepared for the political war over the high court that could dominate the summer, with Senate Minority Leader Charles E. Schumer (D-N.Y.) making his own suggestion for Trump.

Schumer privately urged the president in a phone call earlier this week to nominate federal judge Merrick B. Garland, who was Obama’s third nominee to the Supreme Court and was summarily shunned by Senate Republicans in 2016.

Trump called Schumer on Tuesday afternoon for a Supreme Court-centered conversation that lasted less than five minutes, according to a person familiar with the call. Schumer, the person said, pressed the president to name Garland to succeed Kennedy, arguing that doing so would help unite the country.

Schumer also warned the president that nominating a jurist who would be hostile to Roe v. Wade, the landmark 1973 decision that established a woman’s right to an abortion, and to Obama’s health-care law would be “cataclysmic” and damage Trump’s legacy, added the person, who was not authorized to speak publicly and requested anonymity.

During the 2016 presidential campaign, Trump pledged to nominate judges who would overturn Roe v. Wade.

Schumer also tweeted barbs about Kethledge on Thursday. “Judge Kethledge has a history of opposing women’s reproductive freedom,” he wrote.

The rush of scrutiny gave Kethledge’s backers hope that his chances were perhaps rising — and a preview of the political firestorm he would face on Capitol Hill should he be nominated.